A325198 Positive numbers whose maximum prime index minus minimum prime index is 2.

10, 20, 21, 30, 40, 50, 55, 60, 63, 80, 90, 91, 100, 105, 120, 147, 150, 160, 180, 187, 189, 200, 240, 247, 250, 270, 275, 300, 315, 320, 360, 385, 391, 400, 441, 450, 480, 500, 525, 540, 551, 567, 600, 605, 637, 640, 713, 720, 735, 750, 800, 810, 900, 945

Offset: 1

Author

Gus Wiseman, Apr 11 2019

Keywords

• nonn

Comments

Also Heinz numbers of integer partitions whose maximum minus minimum part is 2 (counted by A008805). The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Examples

			The sequence of terms together with their prime indices begins:
   10: {1,3}
   20: {1,1,3}
   21: {2,4}
   30: {1,2,3}
   40: {1,1,1,3}
   50: {1,3,3}
   55: {3,5}
   60: {1,1,2,3}
   63: {2,2,4}
   80: {1,1,1,1,3}
   90: {1,2,2,3}
   91: {4,6}
  100: {1,1,3,3}
  105: {2,3,4}
  120: {1,1,1,2,3}
  147: {2,4,4}
  150: {1,2,3,3}
  160: {1,1,1,1,1,3}
  180: {1,1,2,2,3}
  187: {5,7}
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Positions of 2's in A243055.

A061395(a(n)) - A055396((n)) = 2.

Cf. A000961, A008805, A046660, A056239, A093641, A112798, A118914, A174090, A195086, A256617, A325180, A325197.

Programs

Maple

N:= 1000: # for terms <= N
q:= 2: r:= 3:
Res:= NULL:
do
  p:= q; q:= r; r:= nextprime(r);
  if p*r > N then break fi;
  for i from 1 do
    pi:= p^i;
    if pi*r > N then break fi;
    for j from 0 do
      piqj:= pi*q^j;
      if piqj*r > N then break fi;
      Res:= Res, seq(piqj*r^k,k=1 .. floor(log[r](N/piqj)))
    od
  od
od:
sort([Res]); # Robert Israel, Apr 12 2019

Mathematica

Select[Range[100],PrimePi[FactorInteger[#][[-1,1]]]-PrimePi[FactorInteger[#][[1,1]]]==2&]